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CFApprox, CFApproximants, ContFrac

Syntax

CFApprox(X:RAT, Prec:RAT): RAT
CFApproximants(X:RAT): LIST of INT and RAT
ContFrac(X:RAT):LIST of INT
    

Summary

continued fractions

Description

CFApprox finds the simplest rational approximation within a maximum specified relative error. CFApproximants returns a list of all continued fraction approximants to a specified rational ContFrac returns a list of the continued fraction denominators for a given rational number.

example

    
CFApprox(1.414213, 10^(-2));
17/12
-------------------------------
CFApproximants(1.414213);
[1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 816/577, 1393/985, 
 6388/4517, 7781/5502, 14169/10019, 21950/15521, 36119/25540, 58069/41061, 
 152257/107662, 210326/148723, 1414213/1000000]
-------------------------------
ContFrac(1.414213);
[1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 6]
-------------------------------